Question

Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an left bracket, x, comma, y, right bracket(x,y) point.
y=−x^2+6x−18

Answer 1

To find the coordinates of the vertex of the parabola, we need to first rewrite the given quadratic function in vertex form.

The vertex form of a quadratic function is y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.

Given quadratic function: y = -x^2 + 6x - 18

To rewrite this function in vertex form, we first complete the square for the x^2 term and x term:

y = -(x^2 - 6x) - 18
y = -(x^2 - 6x + 9) - 18 + 9
y = -(x-3)^2 - 9

Now the given function is in vertex form with the vertex (h, k) = (3, -9)

Therefore, the coordinates of the vertex of the parabola are (3, -9).